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arXiv · 1303.2332

K-stability and parabolic stability

Yann Rollin
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Abstract

Parabolic structures with rational weights encode certain iterated blowups of geometrically ruled surfaces. In this paper, we show that the three notions of parabolic polystability, K-polystability and existence of constant scalar curvature K\"ahler metrics on the iterated blowup are equivalent, for certain polarizations close to the boundary of the K\"ahler cone.

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Yann Rollin. 2013-03-10. K-stability and parabolic stability. https://arxiv.org/abs/1303.2332

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